Motivic-cycle realization conjecture for regularized theta lifts

Let $A^j_{\eta}$ be the $j$-fold power of the universal elliptic-curve family over the generic point $\eta$, and let $H^{2j+1}_{\mathcal M}(A^j_{\eta},\mathds Q(j+1))_{\mathrm{ind}}$ denote the indicated indecomposable motivic cohomology group. Let $f$ be a weakly holomorphic modular form of weight $\frac12-j$ and representation $\rho_L$, and let $\Phi^j(y,f)$ be the regularized theta lift. Motivic-cycle realization conjecture. There is a motivic cycle $\xi_f$ in

$$H^{2j+1}_{\mathcal M}(A^j_{\eta},\mathds Q(j+1))_{\mathrm{ind}}$$

such that

$$\langle\operatorname{reg}(\xi_f),\eta_y^j\rangle=\Phi^j(y,f).$$

This conjecture proposes that the image of the regulator map from motivic cycles agrees with the image of the regularized theta-lift construction, linking motivic cohomology and harmonic Maass-form theory. The source does not state a resolution.